Forming limit stresses predicted by phenomenological plasticity theories with anisotropic work-hardening behavior

Forming limit stresses of sheet metals subjected to linear and combined stress paths are analyzed using the M-K model in conjunction with two anisotropic work-hardening models: a work-hardening model which is capable of describing Bauschinger and cross-hardening effects, and a work-hardening model which cannot predict the cross-hardening effect. It is found that the forming limit stress is path-independent when the stress–strain curves for the linear and combined stress paths agree well with each other. On the other hand, the forming limit stress for the combined stress path depends on the strain path when the prestrain changes the subsequent stress–strain relation. We conclude that the stress-based forming limit criterion is efficient only for a material with a work-hardening behavior that is not affected by strain path change. The influence of the work-hardening behavior on the forming limit stress is discussed in detail.     

Deformation,temperature and strain rate sequence experiments on OFHC Cu

In this paper, we report a series of large strain deformation experiments on initially annealed oxygen-free high conductivity (OFHC) Cu involving sequences of deformation path, temperature, and strain rate (quasi-static to dynamic). Experiments were conducted to obtain a comprehensive data set for the development and evaluation of internal state variable (ISV) models and for the investigation of different functional forms for internal state variable evolution. These included: (a) constant true strain rate tests at various temperatures, (b) load–unload–hold–reload tests at several nominal temperatures, and (c) sequence tests, including strain rate changes, temperature changes and deformation path changes. OFHC Cu demonstrates sensitivity to strain rate and temperature, and exhibits significant history effects. Implications of these data are discussed for the evaluation and development of models which account for deformation path, temperature, and strain rate history effects.     

Multiscale experimental investigations about the cyclic behavior of the 304L SS

This work follows a series of experiments carried out earlier at INSA of Rouen (Hassan, T., Taleb, L., Krishna, S., 2008. Influence of non-proportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plast. 24, 1863–1889). It investigates the elastoplastic cyclic behavior of a 304L stainless steel at room temperature. In a first step the cross path effect on ratcheting is confirmed, as well as the crucial role of the loading path non-proportionality. Strain controlled tests are also conducted for different strain amplitudes and loading paths. Cross-hardening effect appears more important when the shearing sequence is followed by the axial one. Moreover for alternating axial and shearing cycles, this phenomenon occurs after each crossing sequence leading to a very significant strain hardening, at least of the same order as the one obtained after a circular strain path. Yet, the magnitude of the observed over hardening does not necessarily seem a function of the cumulated plastic strain.     

Review of theoretical models of the strain-based FLD and their relevance to the stress-based FLD

The forming limit diagram (FLD) is used in sheet metal forming analysis to determine how close the sheet metal is to tearing when it is formed into a product shape in a stamping process. The strain-path dependent nature of the FLD causes the method to become ineffective in the analysis of complex forming process, especially restrikes, flanging operations, hydroforming, and even first draw dies with deep pockets or embossments. Experimental evidence for a path-independent stress-based FLD has been reported in the literature, suggesting that the path dependency of the strain-based approach arises from the path dependent constitutive laws governing the relationship between the stress and strain tensors. This paper reviews several theoretical models of sheet metal forming instability, including bifurcation analyses of diffuse and through-thickness neck formation, the M-K model and microscopic void damage models. The equations governing the deformation at the instant of the bifurcation is shown to be independent of path in all of these models, providing a solid theoretical bases for the stress-based approach. The stress-based FLD can now be used equally well for all forming processes, without concern for path effects.     

ON NONPROPORTIONAL CYCLIC PLASTIC BEHAVIOR OF STEEL 40

An experimental investigation was carried out on the flow characteristicand hardening of steel 40 subjected to complex combined axial-torsional cyclicstraining. For a specific cyclic strain path, the steel has mainly cyclic softeningbehavior when the strain amplitude is small. While with an increase of the effectivestrain amplitude, the softening becomes small, but there is the cyclic softening eventhough the steel is subjected to the cyclic loading by a square strain path. However, thesteel has cyclic additional hardening by a nonproportional path, compared with theproportional cycling. Generally, the additional hardening is small and its historicaleffect is not obvious at small strain amplitude. The additional hardening is remarkableby a cross-triangular strain path of large strain amplitude. The memory of the historyof nonproportional cyclic loading, the direction of plastic flow and the plastic modulusof the steel were also studied.     

Thin walled beams with internal unbonded cables: Balance conditions and stability

A technique for controlling the stress and strain state of beams consists in introducing stretched slipping cables at their interior. This provides a coupling between the local cable strain and the global rod deformation which makes conventional rod models based on local balance conditions inapplicable. The paper presents a model for this kind of structural system in order to formulate the elastic problem and to analyse the stability of known balanced configurations. A generic cable path crossing the interior of the rod is considered. Both variational formulation and local formulation are reported; in particular the latter leads to integro-differential equations. Some qualitative aspects related to the particular coupling between the system components and the effect on the cable path geometry on the stability are discussed.     

1Cr18Ni9Ti不锈钢的非比例循环强化性能

对1Cr18Ni9Ti不锈钢进行了各种比例和非比例循环本构实验,其中包括圆路径、正方形、正菱形、蝶形、三角形和两种十字形应变路径。表明其具有明显的非比例循环附加强化。在相同的等效应变幅值上,材料的附加强化与路径密切相关。对于圆路径,其附加强化度最大可达60％。通过对不同应变历史的实验研究表明,先前小的非比例度的加载历史对后继大的非比例度路径的强化没有影响;而先前大非比例度的加载路径对后继小非比例度路径的循环强化有较大影响。     

Influence of Portevin-Le Chatelier Effect on Shear Strain Path Reversal in an Al-Mg Alloy at Room and High Temperatures

The main objective of this study is to characterize the mechanical behaviour of an Al-Mg alloy in conditions close to those encountered during sheet forming processes, i.e. with strain path changes and at strain rates and temperatures in the range 1.2×10^?3–1.2×10^?1 s^?1 and 25–200°C, respectively. The onset of jerky flow and the interaction of dynamic strain ageing with the work-hardening are investigated during reversed-loading in specific simple shear tests, which consist of loading up to various shear strain values followed by reloading in the opposite direction, combined with direct observations of the sample surface using a digital image correlation technique. Both strain path changes and temperature are clearly shown to influence the occurrence and onset of the Portevin-Le Chatelier (PLC) effect. Moreover, the Bauschinger effect observed in the material response shows that the PLC effect has a major influence on the kinematic contribution to work-hardening as well as its stagnation during the reloading stage, which could open up interesting lines of research to improve theoretical plasticity models for this family of aluminium alloys.     

Plastic spin associated with a non-normality theory of plasticity

A plasticity model using a vertex-type plastic flow rule on a smooth yield surface for an anisotropic solid has been proposed recently. This model is here completed by incorporating the effect of plastic spin. Simple shear with a large shear strain is one of the hardest tests on finite strain anisotropic plasticity models, and it is here shown which plastic spin expression is needed to avoid unrealistic oscillatory behavior of the shear stress under large shear strains. The idea of using non-normality with a smooth yield surface originates from a recent proposal of using an abrupt strain path change to determine the subsequent yield surface shape. For this method both polycrystal plasticity calculations and experiments have shown a vertex-type response on the apparently smooth yield surface.     

Experimental investigation of phase-strain-temperature models for structurally embedded interferometric fiber-optic sensors

Analytical models relating the optical phase change in a structurally embedded optical fiber sensor to the strain and temperature state integrated along that sensor path is investigated in this paper. Generalized plane strain elasticity solutions are combined with two phase-strain-temperature models to predict the thermomechanically induced optical retardation of the light propagating in the fiber sensor. These predictions are compared with experimental data obtained from Mach-Zehnder and Fabry-Perot sensors embedded in transverse compression and uniformly heated specimens respectively. Paper was presented at the 1992 SEM Spring Conference held in Las Vegas, NV on June 8–11.     

Atomistic potentials based energy flux integral criterion for dynamic adiabatic shear banding

The energy flux integral criterion based on atomistic potentials within the framework of hyperelasticity–plasticity is proposed for dynamic adiabatic shear banding (ASB). System Helmholtz energy decomposition reveals that the dynamic influence on the integral path dependence is originated from the volumetric strain energy and partial deviatoric strain energy, and the plastic influence only from the rest part of deviatoric strain energy. The concept of critical shear banding energy is suggested for describing the initiation of ASB, which consists of the dynamic recrystallization (DRX) threshold energy and the thermal softening energy. The criterion directly relates energy flux to the basic physical processes that induce shear instability such as dislocation nucleations and multiplications, without introducing ad-hoc parameters in empirical constitutive models. It reduces to the classical path independent J-integral for quasi-static loading and elastic solids. The atomistic-to-continuum multiscale coupling method is used to simulate the initiation of ASB. Atomic configurations indicate that DRX induced microstructural softening may be essential to the dynamic shear localization and hence the initiation of ASB.     

Effect of nonlinear strain paths on forming limits under isotropic and anisotropic hardening

The path-dependence of the conventional Forming Limit Diagram (FLD) is an important issue for its applications in industry. Great efforts have been made to understand the nature of the path-dependence with both experimental and theoretical approaches, many of them attempting to find a path-independent way for the application of forming limits. In this paper, we focus on the nonlinear strain path effect on forming limit predictions using both isotropic and anisotropic hardening models. The Forming Limit Diagram (FLD), Forming Limit Stress Diagram (FLSD) and Forming Limit Effective Strain Diagram (epFLD) of sheet metals subject to linear and nonlinear strain paths are analyzed and compared using the Marciniak–Kuczynski approach. An anisotropic hardening model based on Yoshida and Uemori development is adopted in this study, and it is coupled with the traditional Hill’48 yield surface. This model is capable of describing the complex Bauschinger phenomenon after the material undergoes the reverse loading process such as the early re-yielding, work-hardening stagnation and permanent softening. Two different scenarios for the change of strain paths are also investigated. In the first scenario, the sheet material is initially loaded with a fixed strain increment ratio, unloaded to the free stress state, and then reloaded with a different strain increment ratio until the forming limit is reached. In the second scenario, the material does not undergo elastic unloading. Instead, the strain path is abruptly changed to a different strain increment ratio and the material undergoes continuous loading until the forming limit is reached. It is found that the work-hardening behavior after the pre-straining and the loading scenario plays an important role in the path dependent behavior of forming limits. Detailed analysis reveals that the M–K approach may have contributed to the significance of path-dependence observed in this study, especially at high pre-strain levels.     

40钢非比例循环塑性行为研究

对４０钢在拉扭循环复杂应变路径下的硬化特性和流动特性进行了实验研究。研究表明：４０钢材料的循环硬／软化不但依赖于应变路径形状，而且依赖于等效应变幅值，还具有路径历史效应；材料的塑性流动几乎不受先前路径历史的影响，仅依赖于当前应变路径形状和等效奕变幅值。     

Unloading characteristics of anti-plane shear crack in softening materials

The local characteristics of the anti-plane shear stress and strain field are determined for a material where the stress increases linearly with strain up to a limit and then softens nonlinearly. Two unloading models are considered such that the unloading path always returns to the origin while the other assumes the unloading modulus to be that of the initial shear modulus. As the applied shear increases, an unloading zone is found to prevail between a zone in which the material softens and another zone in which the material is linear-elastic even though the crack does not propagate. The divisions of these zones are displayed graphically.     

Experimental determination of strain-induced anisotropy during nonproportional straining of an A1/Mg alloy at room temperature

A servohydraulic, computer controlled MTSn axial-torsion testing machine with a bi-axial clip-on extensometer is used to test thin-walled tubes of an A1/Mg alloy under strain control. A plastic offset strain of 10⁻⁴ determines the yield surfaces. Straining and yield surface probing is governed by a computer program which also controls digital data acquisition. Yield surfaces in stress and in strain space as well as the axial and shear stress-strain diagrams can be reconstructed from the digitally recorded data. The specimens were subjected to a strain path in the form of a regular 16-sided polygon which was followed on some specimens by a square path. The total inelastic strain path length can exceed 15% while the equivalent strain excursion is less than 2%. It is shown that yield surfaces measured on specimens withclose initial stress-strain diagrams are very consistent and that yield surface probing has an insignificant effect on subsequent yield surfaces. Yield surfaces are shown to translate, changein shape and size and to exhibit a cross effect. A post processor which includes a least square smoothing routine calculates the area and the centroid of each yield surface. The size increase is initially rapid but the rate of increase decreases as a saturation is approached. After strining for less than 1% in a fixed direction a characteristic yield surface shape is established. Yield surfaces obtained at the same point in strain space with identical prestrain direction of at least 1% but with increased amounts of accumulated plastic strain have the same shape but show an increase in size. The yield surfaces differ in shape and size when the same strain point is reached from different directions. The centroid of the yield surface in stress space moves almost in a circular path for a polygonal strain path. All stress space yield surfaces contain the origin but this is not the case for the surfaces in strain space.     

Effects of strain path shapes on non-proportional cyclic plasticity

The title problem was discussed to facilitate the formulation of constitutive models of cyclic plasticity under general states of loading. A series of plastic strain controlled cyclic tests was performed by applying combined axial force and torque to thin-walled tubular specimens of Type 316 stainless steel at room temperature. These tests consist of cyclic loading along uniaxial, torsional, cruciform, stellate in eight directions, square and circular plastic strain paths with a constant amplitude of equivalent plastic strain.The results of these tests showed that the strain-hardening depends markedly on the shape of the plastic strain path, and that the strain-hardening (measured by equivalent stress amplitudes) in the saturated state is significant in the order of circular, square, stellate, cruciform and proportional paths. It was also observed that these saturated values were independent of the less significant plastic strain cycles experienced in the past. Finally, the characteristic features of strain-hardening mechanisms under non-proportional loadings were discussed in some detail on the basis of the present results.     

固体材料不稳定性的特征

基于分析势函数的二次变分,从理论上证明了固体材料不稳定性主要取决于材质不断退化的重要特征。另一特征是：材料往往会由基本变形路径漂移为一个轴向应变被限定的模态以至的失稳。文中以有限元方法计算模拟受周期性分布孔洞损伤的平面板材模型,结果显示,孔周边的应变局部化使变形路径转移到一个轴向应变被限定的失效模态。此类现象与金属板材拉胀实验中所观测到的结果相符合。     

砖砌体双参数单轴受压弹塑性损伤力学模型

参考弹塑性损伤模型理论和相关试验数据,建立了砖砌体单轴单调受压和重复受压两种弹塑性损伤本构模型.在模型中采用抗压强度和峰值压应变双参数来调整形变曲线,从而实现了砖砌体单轴受压本构模型的精细化建立.模型不但与既有弹塑性模型相符,而且还符合受压延性与强度呈反向变化的试验结论.重复受压加-卸载路径建立在卸载线性假定的基础上,参考两组试验数据,得出了双线性抗压刚度劣化函数,并通过强度线性插值来调整劣化速率,从而建立了随强度改变的受压加-卸载损伤本构模型.     

镍基单晶合金多轴非比例加载低周疲劳研究

基于正交设计, 分别在680℃和850℃下进行DD3镍基单晶合金薄壁圆管试样([001]取向)拉/扭非比例加载低周疲劳试验, 研究等效应变范围、应变路径角、拉/扭载荷相位角、循环特性和温度诸因素对镍基单晶合金多轴低周疲劳寿命的影响作用. 疲劳试验数据的极差分析表明, 应变路径角、拉/扭载荷相位角和等效应变范围是影响疲劳寿命的主要因素. 将菱形应变加载路径区分为比例加载段和非比例加载段, 提出了表征非比例加载效应的等效应变参量, 并通过引入单晶应变三轴性因子反映拉/扭应变路径角对多轴疲劳寿命的影响. 用考虑非比例加载效应的等效应变范围和单晶应变三轴性因子构造循环塑性应变能损伤参量, 进行多元线性回归分析, 疲劳寿命回归模型与试验寿命具有很好的相关性, 所有试验数据都落在2.0倍的偏差分布带之内.